BTC

Table Of Statistics (Daily, Returns (%))

BTC (N = 2,081)
Mean (sd) 2,080; 0.22 ± 3.94
median (Q1, Q3) 2,080; 0.19 (-1.21, 1.78)
min -37.16954
max 25.24717
Cumulative Return 466.6306
Normally Distributed VaR -6.25452002497649
Non-Normally Distributed VaR -6.05178991592173

The above statistics table is based on the percentage returns for the daily price valuation of bitcoin; it presents the mean, median, min, and max returns to demonstrate the range as well as the average return over the six year period from 2014 to 2020.

In regards to the mean return (%) of bitcoin, it can be noted that it is positive and relatively close in value to the median price meaning that over a daily basis, bitcoin is expected to provide approximately .22% return of an investment per day during a 6 year period. This can fluctuate depending on the valuation trend as the price of bitcoin can over a larger period be trending downwards, upwards or sideways. Given that the mean and the median are relatively close in value, there is limited skewness in the data, and the skewness is favoring higher returns since the mean is to the right of the median.

Colloquially, a bull market is defined as a financial securitity with a sustained increase in valuation; thus, a bear market is defined as a financial securitity with a sustained decrease in valuation; and a trendless market does not have either a sustained increase or a sustained decrease in valuation.

The standard deviation is approximately 3.94% which means that 95% of the daily returns will most likely fluctuate between [-7.66%, 8.01%]. Anything that occurs outside of this interval would be a rare event with a probability \(\le 5%\), which means that most of the returns would occur be centered around the mean, and 5% of the returns would be \([-\infty,-7.66\%]\cup[8.01\%,\infty]\) (outside of the interval [-7.66%, 8.01%]).

In addition, the minimum provided in this table is the greatest percent decrease in the valuation of bitcoin for a single day, and respectively, the maximum is the greatest percent increase in the valuation of bitcoin for a single day. While the cummulative return is the total percentage return over the full period of the investment.

Finally, the value at risk is approximately 6.25% which means that on a daily time frame, there is a probability of \(5\%\) that one could lose 6.25% on the daily, this is important information for trading and risks could be taken to mitigate the risks of a 6.25% drawback in one’s portfolio through hedging or other means.

Plotting Returns (Daily, Returns)

There two figure presented above is a representation of the returns plotted against time which denotes the returns for each of the change in price valuation on the daily basis. In addition, the histogram represents the frequency for the returns within a .5% interval, and based on the graph there are some outlier in the distribution but it is mostly centered around the mean and it has a gaussian shape meaning that the returns are normally distributed. This can be tested using a form of normality test but will not given the visual shape of the data.

#Financial projections of Bitcoin: {.tabset}

BTC With Historical Statistics Used for the Deterministic Projection of Logarithmic Growth

Simple Price Projection with Geometric Brownian Motion

## [1] 0.0003255208

Multiple Price Projections with Geometric Brownian Motion

When simulating the data,

Subsetting the data Into 6 groups:

Major Bull Market

BullMarket (N = 1,068)
Mean (sd) 0.49 ± 3.72
median (Q1, Q3) 0.27 (-0.78, 1.83)
min -21.14486
max 25.24717
Cumulative Return 520.3815
Normally Distributed VaR -5.6378883280451
Non-Normally Distributed VaR -5.35477918110908

Major Bear Market

BearMarket (N = 894)
Mean (sd) 0.01 ± 4.18
median (Q1, Q3) 0.10 (-1.66, 1.63)
min -37.16954
max 18.18776
Cumulative Return 8.210591
Normally Distributed VaR -6.87117808582232
Non-Normally Distributed VaR -6.45995118699981

Minor Bear Market 1

FirstMinorBearMarket (N = 363)
Mean (sd) -0.40 ± 4.39
median (Q1, Q3) -0.01 (-2.38, 1.46)
min -16.8548
max 14.78049
Cumulative Return -143.6408
Normally Distributed VaR -7.61358726528272
Non-Normally Distributed VaR -8.58836887321155

Minor Bull Market 1

FirstMinorBullMarket (N = 194)
Mean (sd) 0.78 ± 3.46
median (Q1, Q3) 0.32 (-0.63, 1.91)
min -8.831367
max 17.35601
Cumulative Return 150.7003
Normally Distributed VaR -4.91756452906168
Non-Normally Distributed VaR -4.72327966403773

Minor Bear Market 2

SecondMinorBearMarket (N = 261)
Mean (sd) -0.23 ± 4.23
median (Q1, Q3) -0.21 (-1.79, 1.32)
min -37.16954
max 15.57634
Cumulative Return -60.61308
Normally Distributed VaR -7.18986945691556
Non-Normally Distributed VaR -5.56762480911872

Minor Bull Market 2

SeconMinorBullMarket (N = 2,003)
Mean (sd) 2,002; 0.22 ± 3.82
median (Q1, Q3) 2,002; 0.19 (-1.21, 1.74)
min -21.14486
max 25.24717
Cumulative Return 431.644
Normally Distributed VaR -6.07594799566695
Non-Normally Distributed VaR -6.04638976371344

Results of 500 simulated Prices Projections

##      Min.   1st Qu.    Median      Mean   3rd Qu.      Max. 
##      27.8    2978.1    9921.5   45473.0   30992.1 3081023.7
##           5%          10%          15%          20%          25%          30% 
##     641.5792    1064.0722    1586.3620    2176.9280    2978.0662    3973.6076 
##          35%          40%          45%          50%          55%          60% 
##    5155.1599    6341.4031    8186.7371    9921.5147   12009.6031   15296.2046 
##          65%          70%          75%          80%          85%          90% 
##   19908.2748   23702.6301   30992.0557   41590.4879   58419.2534   88290.1358 
##          95%         100% 
##  153157.3189 3081023.7194